Algebra Examples

$\sqrt{72} + \sqrt{32} + \sqrt{18}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $72$ as $6^{2} \cdot 2$ .

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Step 1.1.1

Factor $36$ out of $72$ .

$\sqrt{36 (2)} + \sqrt{32} + \sqrt{18}$

Step 1.1.2

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 2} + \sqrt{32} + \sqrt{18}$

$\sqrt{6^{2} \cdot 2} + \sqrt{32} + \sqrt{18}$

Step 1.2

Pull terms out from under the radical.

$6 \sqrt{2} + \sqrt{32} + \sqrt{18}$

Step 1.3

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 1.3.1

Factor $16$ out of $32$ .

$6 \sqrt{2} + \sqrt{16 (2)} + \sqrt{18}$

Step 1.3.2

Rewrite $16$ as $4^{2}$ .

$6 \sqrt{2} + \sqrt{4^{2} \cdot 2} + \sqrt{18}$

$6 \sqrt{2} + \sqrt{4^{2} \cdot 2} + \sqrt{18}$

Step 1.4

Pull terms out from under the radical.

$6 \sqrt{2} + 4 \sqrt{2} + \sqrt{18}$

Step 1.5

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 1.5.1

Factor $9$ out of $18$ .

$6 \sqrt{2} + 4 \sqrt{2} + \sqrt{9 (2)}$

Step 1.5.2

Rewrite $9$ as $3^{2}$ .

$6 \sqrt{2} + 4 \sqrt{2} + \sqrt{3^{2} \cdot 2}$

$6 \sqrt{2} + 4 \sqrt{2} + \sqrt{3^{2} \cdot 2}$

Step 1.6

Pull terms out from under the radical.

$6 \sqrt{2} + 4 \sqrt{2} + 3 \sqrt{2}$

$6 \sqrt{2} + 4 \sqrt{2} + 3 \sqrt{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $6 \sqrt{2}$ and $4 \sqrt{2}$ .

$10 \sqrt{2} + 3 \sqrt{2}$

Step 2.2

Add $10 \sqrt{2}$ and $3 \sqrt{2}$ .

$13 \sqrt{2}$

$13 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$13 \sqrt{2}$

Decimal Form:

$18.38477631 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$